Search

Process mining is shifting towards use cases that explicitly leverage the relations between data objects and events under the term of object-centric process mining. Realizing this shift and generally simplifying the exchange and transformation of data between source systems and process mining solutions requires a standardized data format for such object-centric event data (OCED). This report summarizes the activities and results for identifying requirements and challenges for a community-supported standard for OCED. (1) We present a proposal for a core model for object-centric event data that underlies all known use cases. (2) We detail the limitations of the core model wrt. a broad range of use cases and discuss how to overcome them through conventions, usage patterns, and extensions of OCED, exhausting the design-space for an OCED data model and the inherent trade-offs in representing object-centric event data. (3) These insights are backed by five independent OCED implementations which are presented alongside a series of lessons learned in academic and industrial case studies. The results of this report provide guidance to the community to start adopting and building new process mining use cases and solutions around the reliable concepts for object-centric event data, and to engage in a structured process for standardizing OCED based on the known OCED design space., Comment: 46 pages, 11 figures, report of the OCED working group of the IEEE Taskforce on Process Mining towards the development of a new standard for exchange and storage of object-centric event data

This paper introduces a novel approach that integrates future closest point predictions into the distance constraints of a collision avoidance controller, leveraging convex hulls with closest point distance calculations. By addressing abrupt shifts in closest points, this method effectively reduces collision risks and enhances controller performance. Applied to an Image Guided Therapy robot and validated through simulations and user experiments, the framework demonstrates improved distance prediction accuracy, smoother trajectories, and safer navigation near obstacles.

Models for quantum state reduction address the quantum measurement problem by suggesting weak modifications to Schr\"odinger's equation that have no observable effect at microscopic scales, but dominate the dynamics of macroscopic objects. Enforcing linearity of the master equation for such models ensures that modifications to Schr\"odinger's equation do not introduce a possibility for superluminal signalling. In large classes of quantum state reduction models, however, and in particular in all models employing correlated noise, formulating a master equation for the quantum state is prohibitively difficult or impossible. Here, we formulate a witness for superluminal signalling that is applicable to generic quantum state reduction models, including those involving correlated noise. We apply the witness to several relevant cases, and find that correlated-noise models in general allow for superluminal signalling. We suggest how specific models may be able to avoid it, and that the witness introduced here provides a stringent guide to constructing such models., Comment: 6 pages, 2 figures

The cognitive mechanisms underlying subjects' self-regulation in Brain-Computer Interface (BCI) and neurofeedback (NF) training remain poorly understood. Yet, a mechanistic computational model of each individual learning trajectory is required to improve the reliability of BCI applications. The few existing attempts mostly rely on model-free (reinforcement learning) approaches. Hence, they cannot capture the strategy developed by each subject and neither finely predict their learning curve. In this study, we propose an alternative, model-based approach rooted in cognitive skill learning within the Active Inference framework. We show how BCI training may be framed as an inference problem under high uncertainties. We illustrate the proposed approach on a previously published synthetic Motor Imagery ERD laterality training. We show how simple changes in model parameters allow us to qualitatively match experimental results and account for various subject. In the near future, this approach may provide a powerful computational to model individual skill learning and thus optimize and finely characterize BCI training., Comment: 9th International Graz Brain-Computer Interface Conference 2024, Sep 2024, Graz, Austria

Graph reconstruction can efficiently detect the underlying topology of massive networks such as the Internet. Given a query oracle and a set of nodes, the goal is to obtain the edge set by performing as few queries as possible. An algorithm for graph reconstruction is the Simple algorithm (Mathieu & Zhou, 2023), which reconstructs bounded-degree graphs in $\tilde{O}(n^{3/2})$ queries. We extend the use of this algorithm to the class of geometric random graphs with connection radius $r \sim n^k$, with diverging average degree. We show that for this class of graphs, the query complexity is $\tilde{O}(n^{2k+1})$ when k > 3/20. This query complexity is up to a polylog(n) term equal to the number of edges in the graph, which means that the reconstruction algorithm is almost edge-optimal. We also show that with only $n^{1+o(1)}$ queries it is already possible to reconstruct at least 75% of the non-edges of a geometric random graph, in both the sparse and dense setting. Finally, we show that the number of queries is indeed of the same order as the number of edges on the basis of simulations., Comment: 21 pages, 8 figures

We provide an evaluation of an analytical workload in a confidential computing environment, combining DuckDB with two technologies: modular columnar encryption in Parquet files (data at rest) and the newest version of the Intel SGX Trusted Execution Environment (TEE), providing a hardware enclave where data in flight can be (more) securely decrypted and processed. One finding is that the "performance tax" for such confidential analytical processing is acceptable compared to not using these technologies. We eventually manage to run TPC-H SF30 with under 2x overhead compared to non-encrypted, non-enclave execution; we show that, specifically, columnar compression and encryption are a good combination. Our second finding consists of dos and don'ts to tune DuckDB to work effectively in this environment. There are various performance hazards: potentially 5x higher cache miss costs due to memory encryption inside the enclave, NUMA penalties, and highly elevated cost of swapping pages in and out of the enclave -- which is also triggered indirectly by using a non-SGX-aware malloc library.

The fine-grained complexity of computing the Fr\'echet distance has been a topic of much recent work, starting with the quadratic SETH-based conditional lower bound by Bringmann from 2014. Subsequent work established largely the same complexity lower bounds for the Fr\'echet distance in 1D. However, the imbalanced case, which was shown by Bringmann to be tight in dimensions $d\geq 2$, was still left open. Filling in this gap, we show that a faster algorithm for the Fr\'echet distance in the imbalanced case is possible: Given two 1-dimensional curves of complexity $n$ and $n^{\alpha}$ for some $\alpha \in (0,1)$, we can compute their Fr\'echet distance in $O(n^{2\alpha} \log^2 n + n \log n)$ time. This rules out a conditional lower bound of the form $O((nm)^{1-\epsilon})$ that Bringmann showed for $d \geq 2$ and any $\varepsilon>0$ in turn showing a strict separation with the setting $d=1$. At the heart of our approach lies a data structure that stores a 1-dimensional curve $P$ of complexity $n$, and supports queries with a curve $Q$ of complexity~$m$ for the continuous Fr\'echet distance between $P$ and $Q$. The data structure has size in $\mathcal{O}(n\log n)$ and uses query time in $\mathcal{O}(m^2 \log^2 n)$. Our proof uses a key lemma that is based on the concept of visiting orders and may be of independent interest. We demonstrate this by substantially simplifying the correctness proof of a clustering algorithm by Driemel, Krivo\v{s}ija and Sohler from 2015.

We study the Fr\'echet queries problem. It is a data structure problem, where we are given a set $S$ of $n$ polygonal curves and a distance threshold $\rho$. The data structure should support queries with a polygonal curve $q$ for the elements of $S$, for which the continuous Fr\'echet distance to $q$ is at most $\rho$. Afshani and Driemel in 2018 studied this problem for two-dimensional polygonal curves and gave upper and lower bounds on the space-query time tradeoff. We study the case that the ambient space of the curves is one-dimensional and show an intimate connection to the well-studied rectangle stabbing problem. Here, we are given a set of hyperrectangles as input and a query with a point $q$ should return all input rectangles that contain this point. Using known data structures for rectangle stabbing or orthogonal range searching this directly leads to a data structure with $\mathcal{O}(n \log ^{t-1} n)$ storage and $\mathcal{O}(\log^{t-1} n+k)$ query time, where $k$ denotes the output size and $t$ can be chosen as the maximum number of vertices of either (a) the stored curves or (b) the query curves. The resulting bounds improve upon the bounds by Afshani and Driemel in both the storage and query time. In addition, we show that known lower bounds for rectangle stabbing and orthogonal range reporting with dimension parameter $d= \lfloor t/2 \rfloor$ can be applied to our problem via reduction. .

Methods to generate realistic non-stationary demand scenarios are a key component for analyzing and optimizing decision policies in supply chains. Typical forecasting techniques recommended in standard inventory control textbooks consist of some form of simple exponential smoothing (SES) for both the estimates for the mean and standard deviation. We study demand generating processes (DGPs) that yield non-stationary demand scenarios, and that are consistent with SES, meaning that SES yields unbiased estimates when applied to the generated demand scenarios. As demand in typical practical settings is discrete and non-negative, we study consistent DGPs on the non-negative integers. We derive conditions under which the existence of such DGPs can be guaranteed, and propose a specific DGP that yields autocorrelated, discrete demands when these conditions are satisfied. Our subsequent simulation study gains further insights into the proposed DGP. It demonstrates that from a given initial forecast, our DGPs yields a diverse set of demand scenarios with a wide range of properties. To show the applicability of the DGP, we apply it to generate demand in a standard inventory problem with full backlogging and a positive lead time. We find that appropriate dynamic base-stock levels can be obtained using a new and relatively simple algorithm, and we demonstrate that this algorithm outperforms relevant benchmarks.

Having previously been the subject of decades of semiconductor research, cadmium arsenide has now reemerged as a topological material, realizing ideal three-dimensional Dirac points at the Fermi level. These topological Dirac points lead to a number of extraordinary transport phenomena, including strong quantum oscillations, large magnetoresistance, ultrahigh mobilities, and Fermi velocities exceeding graphene. The large mobilities persist even in thin films and nanowires of cadmium arsenide, suggesting the involvement of topological surface states. However, computational studies of the surface states in this material are lacking, in part due to the large 80-atom unit cell. Here we present the computed Fermi arc surface states of a cadmium arsenide thin film, based on a tight-binding model derived directly from the electronic structure. We show that despite the close proximity of the Dirac points, the Fermi arcs are very long and straight, extending through nearly the entire Brillouin zone. The shape and spin properties of the Fermi arcs suppress both back- and side- scattering at the surface, which we show by explicit integrals over the phase space. The introduction of a small symmetry-breaking term, expected in a strong electric field, gaps the electronic structure, creating a weak topological insulator phase that exhibits similar transport properties. Crucially, the mechanisms suppressing scattering in this material differ from those in other topological materials such as Weyl semimetals and topological insulators, suggesting a new route for engineering high-mobility devices based on Dirac semimetal surface states., Comment: 8 pages, 5 figures